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Файл:Microeconomics. Collection of Tasks and Cases = Микроэкономика. Сборник задач и кейсов. Учебно-методическое пособие
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Negative externality occurs when the activity of one economic agent
Examples of task solutions
causes costs for others.
Positive externality occurs when the activities of one economic agent
bring benefits to others.
Corrective tax is a tax on the production of a good by which marginal
private costs rise to the level of marginal social costs, causing increase of prices
and reduction of output.
Corrective subsidy is a subsidy by which marginal private benefits
increase to the level of marginal social benefits, causing increased output.
Task 15.1.
Given:
A chemical company produces products that benefit society and pollute the
environment. Function of the total positive effect without taking into account
environmental pollution is: TSB = 50∙Q – Q2. Private cost function of the
enterprise is: TPC = 2∙Q + Q2. Function of cumulative damage to nature and
society is: TEC = 8Q.
Find:
1) the output and price of the company;
2) the amount of the corrective tax (T) per unit of production;
3) the optimum output and optimum price from the point of view of the whole
society;
4) the public losses from negative externality;
5) the amount of the corrective tax.
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Solution:
1) The producer's equilibrium point is point
E (Fig. 7). The supply and demand curves
intersect at this point. The demand curve
corresponds to the marginal social benefit,
and the supply curve corresponds to the
marginal private cost. Consequently, to find
the coordinates of the producer equilibrium
point, we need to find the functions MSB
and MPC.
Fig. 7. Negative Externality
We can find MSB function as derived from TSB function:
MSB = TSB' = 50 - 2∙Q.
We can to find the MPC function as derived from TPC function:
МРС = TРС = 2 + 2∙Q At the producer's equilibrium point, demand and
supply are equal. Therefore, we equate the functions MSB and MPC.
50 - 2∙Q = 2 + 2∙Q
QE = 12 units.
PE = 50 - 2 ∙ 12 = 26 mu.
So, the equilibrium output (optimum output from the point of view of the
producer) is 12 units and the equilibrium price in this case is 26 mu.
2) Corrective tax is set at a rate equal to the marginal external cost per unit of
output. We can find the marginal external cost as a derivative of the total external
cost:
Т = МЕС = ТЕС’ = 8 mu.
So, the amount of the corrective tax per unit of production is 8 mu.
3) The optimum point for society is point O (Fig. 7). At this point, the demand
curve MSB and the supply curve MSC intersect. We know the function of the
demand curve - it is the MSB function. We can find the MSC function by adding
MPC and MEC:
MSC = МРС + MEC = 2 + 2∙Q + 8 = 10 + 2∙Q.
We will find the equilibrium point (O) after introducing the corrective tax
from equality:
MSB = MSC.
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From here
50 - 2∙Q = 10 + 2∙Q
QO = 10 units.
PO = 50 - 2 ∙ 10 = 30 mu.
So, the optimum output from the point of view of the whole society is 10
units and the equilibrium price in this case is 30 mu.
We see that the equilibrium output is higher than the socially necessary
output and the equilibrium price is lower than the socially necessary price. The
introduction of a corrective tax eliminates these imbalances.
4) The total damage from negative externality is expressed by the area of the
OKE triangle (Fig. 5). Note that КЕ = МЕС = Т = 8 mu. The height of this
triangle, omitted from O on KE, is equal to the difference QЕ – QO = 12 – 10 = 2
units.
Therefore
Public losses = 0.5∙T ∙ (QЕ – QO) = 0.5 ∙ 8 ∙ 2 = 8 mu.
5) We can find the amount of corrective tax by multiplying the tax rate by the
output:
ΣT = Т (QT) ∙ QТ = 8 ∙ 10 = 80 mu.
Task 15.2.
Given:
The function of total social costs (thousand mu) for training one student is:
TSC = 5 + 3∙Q + 0.25∙Q2, where Q is the number of graduates, thousand people
per year. The function of the external positive effect from the activities of
university graduates per year is: ТЕВ = 8∙Q. The marginal benefit function of
universities is: МРВ = 20 – 0.5∙Q.
Find:
1) the equilibrium number of graduates and the cost of education per year;
2) the optimal number of graduates from the position of the whole society
3) the optimal cost of education per year from the point of view of the whole
society;
4) the amount of the corrective subsidy per student (G);
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5) the total amount of the corrective subsidy (ΣG).
1) The producer's equilibrium point is
point E (Fig. 8). The supply and
demand curves intersect at this point.
The demand curve corresponds to the
marginal private benefit (МРВ), and
the supply curve corresponds to the
marginal social cost (MSC).
Fig. 8. Positive Externality
Solution:
The function of the МРВ is known to us. Consequently, to find the
coordinates of the producer equilibrium point, we need to find the functions of
MSC. We can find this function as a derivative of TSC:
МSC = TSC = 3 + 0.5∙Q.
So we have found the function of the supply curve. At the producer's
equilibrium point E, demand and supply are equal. Therefore, we equate the
functions MSC and MPB:
МSC = МРВ.
3 + 0.5∙Q = 20 - 0.5∙Q
QE = 17 thousand graduates.
We know the equilibrium output, so we can calculate the equilibrium price:
PE = 20 – 0.5∙Q = 20 - 0.5 ∙ 17 = 11.5 thousand mu
2) The optimum point for society is point O (Fig. 8). At this point, the demand
curve MSB and the supply curve MSC intersect. We know the function of the
supply curve and we can find the MSB function as MSB = МРВ + MEB.
The function of the МРВ is known to us. We need to find the MEB function.
We can find this function as a derivative of the function TEB:
MEB = ТЕВ = 8 thousand mu.
the optimum point for society as a whole:
Now we can find the MSB function by adding МРВ and MEB:
MSB = 20 - 0.5∙Q + 8 = 28 - 0.5∙Q.
We can now equate the MSB and MSC functions to find the coordinates of
MSB = МSС.
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Then
Tasks for the self-solution
28 - 0.5∙Q = 3 + 0.5∙Q,
25 = Q.
From here
QO = 25 thousand graduates.
Hence the optimal number of graduates from the position of the whole
society is QO = 25 thousand graduates.
3) We know the optimal number of graduates, so we can calculate the optimal
costs of education per year from the point of view of the whole society. To do
this, we will use the supply function:
PO = МSC = 3 + 0.5∙Q = 3 + 0.5 ∙ 25 = 15.5 thousand mu.
Hence the optimal cost of education per year from the point of view of the
whole society is 15.5 thousand mu.
4) The corrective subsidy (G) is set to be equal to the marginal external benefits:
G = MEB = 8 thousand mu.
So, the amount of the corrective subsidy per student is 8 thousand mu.
5) The total amount of subsidy (ΣG) is determined by multiplying the number of
graduates by the amount of subsidy for one graduate:
ΣG = G (QO) ∙ QO = 8 thousand mu ∙ 25 thousand graduates =
= 200 million mu.
Task 15.3.
Given:
The food processing plant produces products that benefit society, expressed by
the function TSB = 400∙Q – 5∙Q2. Its private costs function is TPC = 180∙Q + Q2.
But this plant pollutes the environment. Function of cumulative damage to nature
and society is: TC = 10∙Q + 1,5∙Q2.
75
Find:
1) the equilibrium output of the company;
2) the equilibrium price of the company;
3) the amount of the corrective tax (T) per unit of production;
4) the optimum output from the point of view of the whole society;
5) the optimum price from the point of view of the whole society;
6) the amount of the corrective tax (ΣT).
Task 15.4.
Given:
The function of total social costs (thousand mu) for training one student is:
TSC = 10 + 6∙Q + 0.5∙Q2, where Q is the number of graduates, thousand people
per year. The function of the external positive effect from the activities of
university graduates per year is: ТЕВ = 10∙Q. The marginal benefit function of
universities is: МРВ = 40 – Q.
Find:
1) the equilibrium number of graduates and the cost of education per year;
2) the optimal number of graduates from the position of the whole society
3) the optimal cost of education per year from the point of view of the whole
society;
4) the amount of the corrective subsidy per student (G);
5) the total amount of the corrective subsidy (ΣG).
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Case study
1
Case 15.1.
Market Failure 1
Here is a list of actual and proposed government programs. Each is a
response to one of the justifications for government activity described in the text:
correction of market failure (due to public goods, external costs, external
benefits, or imperfect competition); encouragement or discouragement of
consumption due to consumers not making rational choices; and redistribution of
income.
Task:
In each case, identify the source of demand for the activity described.
1. The Justice Department sought to prevent Microsoft Corporation from
releasing Windows ’98, arguing that the system’s built-in Internet browser
represented an attempt by Microsoft to monopolize the market for browsers.
2. In 2004, Congress considered a measure that would extend taxation of
cigarettes to vendors that sell cigarettes over the Internet.
3. The federal government engages in research to locate asteroids that
might hit the earth, and studies how impacts from asteroids could be prevented.
4. The federal government increases spending for food stamps for people
whose incomes fall below a certain level.
5. The federal government increases benefits for recipients of Social
Security.
6. The Environmental Protection Agency sets new standards for limiting
the emission of pollutants into the air.
7. A state utilities commission regulates the prices charged by utilities that
provide natural gas to homes and businesses.
Rittenberg L., Tregarthen T. Microeconomics Principles. 2012. P 632.
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Case 15.2.
Taxation
Consider three goods, A, B, and C. The prices of all three goods are
determined by demand and supply (that is, the three industries are perfectly
competitive) and equal $100. The supply curve for good A is perfectly elastic;
the supply curve for good B is a typical, upward-sloping curve; and the supply
curve for good C is perfectly inelastic. Suppose the federal government imposes
a tax of $20 per unit on suppliers of each good.
Tasks:
1) Explain and illustrate graphically how the tax will affect the price of
each good in the short run.
2) Show whether the equilibrium quantity will rise, fall, or remain
unchanged.
3) Who bears the burden of the tax on each good in the short run?
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ANSWERS TO THE TASKS FOR SELF-SOLUTION
Part 1. Introduction to Economics
Topic 1. Economics and Economic Systems
Task 1.2.
1) the maximum quantity of good x, which can be produced = 10 units;
2) the maximum quantity of good y, which can be produced = 900 units;
3) the new equation of the PPC, if the new production technology will allow the
production of good y twice as much: 9∙x2 + 0.5∙y = 900.
Topic 3. Market and market Equilibrium
Task 3.3.
1) the equilibrium price = 10 mu;
2) the equilibrium quantity of sales = 20 units;
3) surplus = 25 mu;
4) shortage = 15 mu.
Task 3.4.
1) the equilibrium price = 10 mu;
2) the equilibrium quantity of sales 10 units;
3) the maximum price = 28 mu;
4) the minimum price = 5 mu;
5) the surplus of consumer = 280 mu;
6) the surplus of producer = 50 mu;
7) the public benefit of sellers and buyers = 330 mu.
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Topic 4. Elasticity of Supply and Demand
Task 4.5.
1) QD = 30;
2) QD = 29;
3) the percentage change in the quantity demanded = -0.034;
4) the percentage change in the price = 0.025;
5) . = -1.36 or |1.36|
This product belongs to the group of elastic in price.
Task 4.6.
1) percentage change in the price of "Mars" = 0.078 or 7.8 %;
2) percentage change in demand for Mars = -0.182 or 18.2 %;
3) percentage change in demand for "Snickers" = 0.222 or 22.2 %;
4) the coefficient of cross elasticity of demand for "Snickers" = 0.2846;
5) these are substitute products, because the cross-elasticity coefficient is greater
than zero.
Task 4.7.
1) percentage change in consumer income = 0.222 or 22.2 %;
2) percentage change in demand for boiled sausage = -0.400 or 40.0 %;
3) percentage change in pork demand = 0.364 or 36.4 %;
4) the coefficient of elasticity of demand for income for boiled sausage = -1.80;
5) the coefficient of elasticity of demand for pork income = 1.64;
6) boiled sausage is inferior good (its income-elasticity coefficient is negative),
pork is normal good (its income-elasticity coefficient is positive).
Task 4.8.
1) percentage change in the supply quantity = 0.400 or 40.0 %;
2) the percentage change in the price = 0.316 or 31.6 %;
3) the coefficient of price elasticity of supply = 1.27.
4) the coefficient is more than one; therefore, the supply is elastic in price.
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